The Pluri-Subharmonicity of Dirichlet’s Energy on T(M); T(M) is a Stein Manifold

Abstract

Let: F:N → IR be areal valued function on the complex manifold N. The Levi-form of F at a point z ∈ N is the complex 2-form

$$ \partial \bar \partial F = \frac{{\partial ^2 F\left( z \right)}} {{\partial z^\alpha \partial \bar z^\beta }}dz^\alpha d\bar z^\beta . $$